Mathematics · Primary 3 · Multiplication and Division · Semester 1

Dividing by 6, 7, 8, and 9

Students will use multiplication facts to divide numbers by 6, 7, 8, and 9, understanding division as sharing and grouping.

• MOE Syllabus Outcomes
• MOE: Numbers and Algebra - P3
• MOE: Multiplication and Division - P3

About This Topic

Primary 3 students build division skills by dividing numbers by 6, 7, 8, and 9 using related multiplication facts. They understand division as sharing items equally among groups or forming equal groups from a total. For instance, 42 divided by 7 involves sharing 42 counters into 7 piles or grouping them into sets of 7. Students practise with numbers up to 72 or 81, focusing on quotients and remainders when needed.

This topic aligns with MOE Numbers and Algebra standards for Multiplication and Division. It strengthens fact fluency, inverse operations, and problem-solving. Students answer key questions like how multiplication facts support division, the distinction between sharing and grouping, and verifying answers by multiplying quotient by divisor plus remainder.

Active learning benefits this topic greatly. Manipulatives allow students to see and touch division processes, clarifying abstract links to multiplication. Group activities build confidence through peer explanations, while games turn repetition into fun, leading to deeper retention and fewer errors in application.

Key Questions

1. How does knowing a multiplication fact help you solve a related division problem?
2. What is the difference between sharing equally and making equal groups?
3. How can you check a division answer using multiplication?

Learning Objectives

• Calculate the quotient and remainder when dividing numbers up to 72 by 6, 7, 8, or 9.
• Explain the relationship between multiplication facts and division problems involving divisors 6, 7, 8, and 9.
• Compare and contrast the concepts of 'sharing equally' and 'making equal groups' in division scenarios.
• Verify division answers by applying the inverse operation of multiplication.

Before You Start

Multiplication Facts up to 10 x 10

Why: Students must have a strong recall of multiplication facts to efficiently solve related division problems.

Introduction to Division (Sharing and Grouping)

Why: Students need foundational understanding of division as an operation before tackling larger divisors.

Key Vocabulary

Quotient	The answer to a division problem. For example, in 48 ÷ 6 = 8, the quotient is 8.
Remainder	The amount left over after dividing a number by another number when it cannot be divided equally. For example, in 50 ÷ 6, the remainder is 2.
Sharing Equally	Distributing a total number of items into a specific number of groups so that each group has the same amount.
Making Equal Groups	Forming sets of a specific size from a total number of items, determining how many sets can be made.

Watch Out for These Misconceptions

Common Misconception

Division means only sharing into groups, not forming groups from a total.

What to Teach Instead

Model both with counters: share 24 into 6 groups, then group 24 into sets of 6. Small group discussions help students compare and articulate differences. Hands-on switching between models builds flexible thinking.

Common Misconception

A remainder means the division is wrong or impossible.

What to Teach Instead

Use drawings or objects to show leftovers when dividing unevenly, like 25 ÷ 8. Students physically group and count remainders, then verify with multiplication equations. Peer teaching in pairs reinforces that remainders are valid.

Common Misconception

Division answers do not connect back to multiplication facts.

What to Teach Instead

Matching games pair facts like 9 × 5 = 45 and 45 ÷ 9 = 5. Students explain links aloud in groups, solidifying the inverse relationship. Repeated active matching reduces reliance on guessing.

Active Learning Ideas

Manipulative Sharing: Counter Division

Give each small group 36 to 72 counters and division cards (e.g., 48 ÷ 6). Students share counters equally into the given number of groups, record the quotient, and check by multiplying back. Discuss any remainders using drawings.

30 min·Small Groups

Grouping Relay: Object Sets

In pairs, students receive a total of items like 56 buttons and form as many equal groups of 7, 8, or 9 as possible. They race to record the division fact, then verify with multiplication. Switch roles for multiple rounds.

25 min·Pairs

Fact Family Match: Card Game

Prepare cards with multiplication (e.g., 6 × 7 = 42) and division facts (42 ÷ 6 = 7). In small groups, students match related facts, solve missing numbers, and explain connections. Play multiple rounds with timers.

20 min·Small Groups

Whole Class Check: Division Bingo

Distribute bingo cards with division problems by 6-9. Call out answers; students solve and mark. First to complete a line shares workings, including multiplication checks. Adapt for remainders in advanced rounds.

35 min·Whole Class

Real-World Connections

• A baker needs to divide 72 cookies equally among 8 friends. Knowing division facts helps the baker quickly determine each friend receives 9 cookies.
• A teacher has 56 pencils to put into boxes, with 7 pencils in each box. Using division, the teacher can calculate that 8 boxes are needed.

Assessment Ideas

Quick Check

Present students with a division problem, such as 63 ÷ 7. Ask them to write down the related multiplication fact and then state the answer to the division problem. Observe if they correctly link the two operations.

Exit Ticket

Give each student a card with a division problem (e.g., 49 ÷ 7). Ask them to write two sentences: one explaining how they solved it using multiplication, and one describing if it represents sharing equally or making equal groups.

Discussion Prompt

Pose the question: 'If you have 40 apples and want to put them into bags of 8, how many bags do you need? How would you check your answer?' Facilitate a brief class discussion where students explain their strategies and use multiplication to verify.

Frequently Asked Questions

How do you teach Primary 3 students to relate multiplication facts to division by 6, 7, 8, 9?

Start with known multiplication charts up to 9 × 9. Use fact families: show 6 × 8 = 48, then flip to 48 ÷ 6 = 8. Practise with real objects for sharing or grouping, always checking by multiplying quotient back to original. Daily 10-minute drills with visuals build automaticity.

How can active learning help students master dividing by 7, 8, and 9?

Active methods like manipulatives and games make abstract division concrete. Students physically share counters or match fact cards in groups, experiencing inverse links to multiplication. This engagement cuts errors by 30-40 percent, as peer discussions clarify remainders and checks, fostering confidence over rote practice.

What are common errors when Primary 3 students divide by 6-9?

Errors include confusing sharing with grouping, ignoring remainders, or forgetting multiplication checks. Students may guess quotients without facts or mix up tables like 7s and 8s. Address with targeted manipulatives: model errors publicly, let students correct via grouping, and reinforce daily fact reviews.

How to check division answers using multiplication in P3 math?

Multiply the quotient by the divisor; the product should equal the dividend or dividend minus remainder. For 56 ÷ 8 = 7, check 8 × 7 = 56. Include remainders: 59 ÷ 8 = 7 r3, verify 8 × 7 + 3 = 59. Use number lines or drawings for visual confirmation during lessons.